Computing ideal sceptical argumentation

  • Authors:
  • P. M. Dung;P. Mancarella;F. Toni

  • Affiliations:
  • Division of Computer Science, Asian Institute of Technology, PO Box 2754, Bangkok 10501, Thailand;Dipartimento di Informatica, Università di Pisa, Largo B. Pontecorvo, 3 I-56127 Pisa, Italy;Department of Computing, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

  • Venue:
  • Artificial Intelligence
  • Year:
  • 2007

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Abstract

We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114-159] that is sound for the sceptical grounded semantics.